House Republicans began Friday the long effort to repeal President Obama's health-care law by approving a resolution that cleared the way for next week's vote. They also devoted time toward cleaning up an embarrassing situation involving two lawmakers who missed Wednesday's swearing-in of the 112th Congress.

The House approved the terms of debate for the repeal bill on a 236-to-181 vote, with four Democrats from conservative-leaning districts siding with every GOP lawmaker present. The final vote on repeal is set for Wednesday after seven hours of debate.

Republicans acknowledge that overturning the landmark law is an uphill effort because Senate Democrats - who still hold the majority in that chamber - have no intention of bringing up the repeal measure. But they suggested that Senate Minority Leader Mitch McConnell (R-Ky.) would at least force a vote on the issue by offering the legislation as an amendment to another bill later this spring.

"They're going to figure out a way to have that vote," Rep. Fred Upton (R-Mich.), chairman of the energy and commerce committee, said in an interview.

Upton and other chairmen have been instructed to begin work on their own bills to undo individual portions of the roughly 2,000-page law and to implement some of their own proposals.

Two Republicans, Reps. Mike Fitzpatrick (Pa.) and Pete Sessions (Texas), voted "present" because of the ongoing controversy over their absence from Wednesday's swearing-in.

The two men missed the oath of office because they were attending an event with Fitzpatrick's constituents a few hundred yards away, in the Capitol Visitor Center. They were sworn in Thursday, and after the House approved the health-care rule Friday, it approved a resolution meant to clean up the situation. Votes that Sessions and Fitzpatrick had cast on Wednesday and Thursday - including approving the rules of the chamber and a 5 percent reduction in congressional office allowances - have now been stricken from the Congressional Record.

House Speaker John A. Boehner declined to have the health-care legislation fall under the open, freewheeling process he had pledged during the fall campaign, telling reporters Thursday that the issue had been debated endlessly throughout 2009 and 2010. Instead, Republicans have arranged a straight up-or-down vote on repealing the law.

"Either we're going to wipe the slate clean and start fresh, or we're not," said House Rules Committee Chairman David Dreier (R-Calif.).